About following the pion stop, a time window known as the delayed pion gate (DPG), of is opened. The pion gate is delayed in order to avoid prompt interaction processes such as elastic scatterings or pion charge exchanges. Within this time window, pion beta decay is registered as a detection in coincidence in the shower calorimeter, of the two gamma rays (with energies exceeding the Michel endpoint) which originate from the decay of the neutral pion. Following the delayed pion gate, another time window is opened; however, this time window is mostly sensitive to Michel events as shown in figure and can be used to understand their rate and the energy distribution.
Figure: Time spectra of Michel and events. The Delayed Pion Gate (DPG) is opened ns after a valid stop in order to avoid Prompt (P) interaction processes. and events are registered during the DPG. Following the DPG, the DPG Prime (DPG') is mostly sensitive to Michel decays. The accurate branching ratios are not taken into account in these pictures. The temporal distribution of event is similar to that of the events, the only difference being in the branching ratios of both decays.
Normalization is performed with the events registered within the DPG as the detection in the calorimeter of the single arm showers with total energy exceeding that of the Michel positrons. The relative measurement of the pion beta decay is possible because of the similarity between the showers produced by photons from and by positrons from as shown in figure . As a result, the detector acceptance and response to the events are very similar to those of the events so that the differences in systematic uncertainties are small and manageable. To account for the difference in the branching ratios the events need to be prescaled.
Figure: Simulated calorimeter responses to photons and positrons. The similarity of the responses can be used to do a relative measurement of the pion beta decay rate by normalizing to events and accounting for the differences in the acceptances and the branching ratios.
Experimentally, the pion beta decay rate is given as the ratio:
where is the pion lifetime, the N's represent the respective numbers of good and events and is the prescale factor for the trigger. The above corrections include ratios of the following quantities for the two triggers respectively: